word problem help its about investing?

Question

An account executive deposited $42,000 into two simple interest accounts. On the tax free account the annual simple interest rate is 3.5%, and on the money market fund the annual simple interest rate is 4.5%. How much should be invested in each account so that both accounts earn the same annual interest rate?

Answer 1

Simple interest is when you take your principal and multiply it by your interest - there's no compounding or any fancy stuff - it's a straightforward calculation.

In your case, you want the resulting interest from the two investments to be the same. You're splitting $42,000 into two accounts, and each has a different interest rate. We'll let x be a partial amount, and 42000 - x be the other partial amount, so that when you add them together, you have your initial $42,000:

Interest for Account A = (x)(0.035)
Interest for Account B = (42000 - x)(0.045)

You want the interest to be the same, so set these equal to each other and solve:

0.035x = (42000 - x)(0.045)
0.035x = 1890 - 0.045x
0.08x = 1890
x = 23625

So if you invest $23,625 in the 3.5% account, you'll end up with $826.88 in interest. And if you invest $18,375 in the 4.5% account, you'll also end up with $826.88 (for both, you'll actually end up with $826.875, but I rounded since you can't get half a penny in your account!).